Refocusing pulses and excitation pulses for nmr logging

ABSTRACT

Illustrative embodiments are directed to applying a nuclear magnetic resonance sequence to a substance within an inhomogeneous static magnetic field. Various embodiments include applying a series of refocusing pulses to the substance, each refocusing pulse in the series of refocusing pulses having at least two segments, and a total pulse duration less than or equal to approximately 1.414 times T 180 . Various embodiments can further include applying an excitation pulse to the substance in the inhomogeneous static magnetic field, where the excitation pulse generates an initial magnetization that is aligned with a refocusing axis produced by a refocusing cycle that is performed after the excitation pulse.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a divisional of co-pending U.S. patent applicationSer. No. 13/338,083, filed Dec. 27, 2011, which is incorporated hereinby reference in its entirety.

TECHNICAL FIELD

This invention relates to nuclear magnetic resonance (NMR) and, moreparticularly, to using nuclear magnetic resonance (NMR) for determiningcharacteristics of substances.

BACKGROUND

General background of nuclear magnetic resonance (NMR) well logging isset forth, for example, in U.S. Pat. No. 5,023,551. Briefly, inconventional NMR operation, the spins of nuclei align themselves alongan externally applied static magnetic field. This equilibrium situationcan be disturbed by a pulse of an oscillating magnetic field (e.g. aradio frequency (RF) pulse), which tips the spins away from the staticfield direction. After tipping, two things occur simultaneously. First,the spins precess around the static field at the Larmor frequency, givenby ω₀=γ×B₀, where B₀ is the strength of the static field and γ is thegyromagnetic ratio. Second, the spins return to the equilibriumdirection according to a decay time T₁, which is called the longitudinalrelaxation time constant or spin lattice relaxation time constant. Forhydrogen nuclei, γ/2π=4258 Hz/Gauss, so, for example, for a static fieldof 235 Gauss, the frequency of precession would be 1 MHz. Alsoassociated with the spin of molecular nuclei is a second relaxation timeconstant, T₂, called the transverse relaxation time constant orspin-spin relaxation time constant. At the end of a ninety degreetipping pulse, all the spins are pointed in a common directionperpendicular to the static field, and they all precess at the Larmorfrequency. The net precessing magnetization decays with a time constantT₂ because the individual spins rotate at different rates and lose theircommon phase. At the molecular level, dephasing is caused by randommotions of the spins. The magnetic fields of neighboring spins andnearby paramagnetic centers appear as randomly fluctuating magneticfields to the spins in random motion. In an inhomogeneous field, spinsat different locations precess at different rates. Therefore, inaddition to the molecular spin-spin relaxation of fluids, spatialinhomogeneities of the applied field also cause dephasing. Spatialinhomogeneities in the field can be due to microscopic inhomogeneitiesin the magnetic susceptibility of rock grains or due to the macroscopicfeatures of the magnet.

A widely used technique for acquiring NMR data, both in the laboratoryand in well logging, uses an RF pulse sequence known as the CPMG(Carr-Purcell-Meiboom-Gill) sequence. As is well known, after a waittime that precedes each pulse sequence, a ninety degree pulse causes thespins to start precessing. Then a one-hundred-eighty degree pulse isapplied to cause the spins which are dephasing in the transverse planeto refocus. By repeatedly refocusing the spins usingone-hundred-eighty-degree pulses, a series of “spin echoes” appear, andthe train of echoes is measured and processed. The transverse relaxationtime constant, T₂, or the distribution of multiple T₂s, can be obtainedusing this technique. In well logging, the CPMG sequence istraditionally executed using a set of equipment located “down-hole” in awell bore (in situ). While performing the CPMG sequence in situ allowsfor relatively rapid data gathering, limitations of the equipment andthe environment can make it difficult to obtain accurate down-hole data.For example, due to the limits on equipment power, design constraintsand down-hole conditions, the signal to noise ratio (SNR) for an in situCPMG sequence remains low. This low SNR can impede the gathering andanalysis of useful data about the formation in the ground.

SUMMARY

Illustrative embodiments are directed to applying a nuclear magneticresonance (NMR) sequence to a substance within an inhomogeneous staticmagnetic field. Various embodiments can include applying a series ofrefocusing pulses to the substance, each refocusing pulse in the seriesof refocusing pulses having at least two segments, and a total pulseduration less than or equal to approximately 1.414 times T₁₈₀. As usedherein:

T ₁₈₀=π(γ+B ₁);

where γ is the gyromagnetic ratio of a particle in the substance withinthe inhomogeneous static magnetic field, and B₁ is the maximum amplitudeof the applied radio frequency (RF) field in the area of interest withinthe substance.

Various embodiments can further include applying an excitation pulse tothe substance in the inhomogeneous static magnetic field, where theexcitation pulse generates an initial magnetization that is aligned witha refocusing axis produced by a refocusing cycle that is performed afterthe excitation pulse. The refocusing cycle includes a series of therefocusing pulses disclosed herein.

Illustrative embodiments are directed to a method for applying an NMRsequence. The method includes applying a series of refocusing pulses toa substance within an inhomogeneous static magnetic field, eachrefocusing pulse in the series of refocusing pulses having at least twosegments, and a total pulse duration less than or equal to approximately1.414 times T₁₈₀.

Various embodiments are directed to a method for applying an (NMR)sequence. The method includes applying a series of refocusing pulses toa substance within an inhomogeneous static magnetic field. Eachrefocusing pulse in the series of refocusing pulses can have thefollowing properties: an initial segment and a final segment each havingsubstantially equal durations, and a middle segment having a durationdistinct from the initial and final segments. The initial segment, themiddle segment, and the final segment each have a substantially constantamplitude, and a phase of the middle segment is shifted 180 degrees withrespect to a phase of each of the initial segment and the final segment.

Illustrative embodiments are directed to a method for applying an NMRsequence. The method includes applying an excitation pulse to asubstance within an inhomogeneous static magnetic field to induce a spineffect within the substance. The excitation pulse includes a pluralityof segments. The method can further include applying a refocusing cycleto the substance, where the refocusing cycle generates a magnetizationin the substance that is aligned with a refocusing axis. The excitationpulse generates an initial magnetization that is aligned with therefocusing axis.

Various embodiments are directed to a method for applying an NMRsequence. The method includes applying an excitation pulse to asubstance within an inhomogeneous static magnetic field to induce a spineffect within the substance. The excitation pulse includes a pluralityof segments, where each of the segments has a substantially constantamplitude. Further, each of the segments has one phase selected from nomore than two distinct phases. The method further includes applying aseries of refocusing pulses to the substance within the inhomogeneousstatic magnetic field after application of the excitation pulse.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages will become more readily apparent fromthe following detailed description when taken in conjunction with theaccompanying drawings.

FIG. 1 shows a schematic diagram, partially in block form, of a welllogging apparatus that can be used in practicing some embodiments of thedisclosure;

FIG. 2 shows a block diagram of downhole circuitry in accordance withvarious embodiments of the disclosure;

FIG. 3 shows a plot of a conventional refocusing pulse and a pluralityof refocusing pulses in accordance with various embodiments of thedisclosure;

FIG. 4 shows a plot of segment values for refocusing pulses inaccordance with various embodiments of the disclosure;

FIG. 5 shows a plot of pulse distributions for a conventional refocusingpulse and for a plurality of refocusing pulses in accordance withvarious embodiments of the disclosure;

FIG. 6 shows a plot of echo shapes for a conventional refocusing pulseand for a plurality of refocusing pulses in accordance with variousembodiments of the disclosure;

FIG. 7 shows Table 1, which shows signal-to-noise ratio (SNR), under twodifferent assumptions of initial excitation, for a conventionalrefocusing pulse and for a plurality of refocusing pulses in accordancewith various embodiments of the disclosure;

FIG. 8 shows a plot of SNR for a conventional refocusing pulse and for aplurality of refocusing pulses in accordance with various embodiments ofthe disclosure;

FIG. 9 shows a plot for an excitation pulse in accordance with variousembodiments of the disclosure;

FIG. 10 shows a plot of echo shapes generated by a conventionalrefocusing pulse and a refocusing pulse in accordance with variousembodiments of the disclosure;

FIG. 11 shows a plot of excitation pulse A in accordance with variousembodiments of the disclosure;

FIG. 12 shows Table 2, which include phase values (in degrees) for eachsegment of excitation pulse A, in accordance with various embodiments ofthe present disclosure;

FIGS. 13-18 shows Tables 3-8, which include phase values (in degrees)for each segment of excitation pulse B, C, D, E, F, and G, respectively,in accordance with various embodiments of the present disclosure;

FIG. 19 shows Table 9, which compares simulated and measured SNR forvarious embodiments of the present disclosure;

FIG. 20 shows a plot of an asymptotic magnetization signal and a plot ofa time-domain echo signal, generated in accordance with variousembodiments of the present disclosure;

FIG. 21 shows Table 10, which includes segment lengths of excitationpulses in accordance with various embodiments of the disclosure;

FIG. 22 shows Table 11, which includes echo characteristics generated bythe excitation pulses defined in FIG. 21;

FIG. 23 shows a plot of segment number by segment length for excitationpulses in accordance with various embodiments of the disclosure;

FIG. 24 shows a plot of a squared echo integral for a conventionalrefocusing pulse and for a plurality of refocusing pulses in accordancewith various embodiments of the disclosure;

FIG. 25 shows a flow diagram illustrating processes in a method inaccordance with various embodiments of the disclosure; and

FIG. 26 shows an illustrative environment for performing NMR processesin accordance with various embodiments of the disclosure.

It is understood that the drawings of the disclosure are not necessarilyto scale.

DETAILED DESCRIPTION OF THE INVENTION

As noted herein, using CPMG sequences to obtain data about substancescan be limited by a low signal-to-noise ratio (SNR). In contrast toconventional approaches, some embodiments of the invention includeutilizing excitation and/or refocusing pulses to improve the SNR in CPMGsequencing, while maintaining the conventional output power of thepulsing equipment. In various embodiments, a class of refocusing pulsesdisclosed herein nearly doubles the SNR in a CPMG sequence as comparedto the conventional approach. Additionally, in some embodiments, anexcitation pulse is utilized which can optimize the SNR gain of therefocusing pulse and can augment the size of the reliable sample slicein the sub stance.

Various embodiments of the invention can be employed using a welllogging apparatus to investigate, in situ, a region of earth formationssurrounding a borehole to determine a characteristic of the region(including e.g., rock, liquid, or some other substance or material).FIG. 1 illustrates an embodiment of such an apparatus for investigatingsubsurface formations 31 traversed by a borehole 32. A magneticresonance investigating apparatus or logging device 30 is suspended inthe borehole 32 on an armored cable 33, the length of whichsubstantially determines the relative depth of the device 30. The lengthof cable 33 is controlled by suitable means at the surface such as adrum and winch mechanism (not shown). Surface equipment, represented at7, can be of conventional type, and can include a processor subsystem incommunication with the downhole equipment. The processor subsystem maybe any suitable NMR equipment of conventional type that can produce asubstantially uniform static magnetic field and can produce radiofrequency (RF) pulses at controlled times and of controlled frequency,phase, and duration as described herein. It will be understood thatprocessing can be performed downhole and/or uphole, and that some of theprocessing may be performed at a remote location. Also, while a wirelineis illustrated, alternative forms of physical support and communicatinglink can be used, for example in a measurement while drilling system(e.g., logging-while-drilling). As described for example in the U.S.Pat. No. 5,055,787, the magnetic resonance logging device 30 can have aface 14 shaped to intimately contact the borehole wall, with minimalgaps or standoff. The borehole wall may have a mudcake 16 thereon. Aretractable arm 15 can be provided which can be activated to press thebody of the tool 13 against the borehole wall during a logging run, withthe face 14 pressed against the wall's surface. Although the tool 13 isshown as a single body, the tool may alternatively comprise separatecomponents such as a cartridge, sonde or skid, and the tool may becombinable with other logging tools.

The logging device includes, for example, a permanent magnet orpermanent magnet array 22, which may comprise samarium-cobalt magneticmaterial, and one or more RF antennas 24, which may be a suitablyoriented coil or coils. A sensitivity zone, represented generally at 27,is a region in the subsurface formations 31 in which the static magneticfield is substantially uniform. An area of interest, representedgenerally at 29, is a region in the subsurface formations 31 in whichthe static magnetic field is inhomogeneous.

FIG. 2 shows, in simplified form, circuitry of a type that can be usedfor producing RF pulse sequences and for receiving and processing NMRsignals as described herein. In FIG. 2, a downhole processor subsystemis represented at 210. The processor subsystem 210 has associatedmemory, timing, interfaces, and peripherals (not separately shown), asis well known in the art. The processor subsystem 210 is conventionallycoupled with telemetry circuitry 205, for communication with the earth'ssurface. An oscillator 220 produces radio frequency (RF) signals at thedesired resonant frequency or frequencies in the investigation region,and the output of the oscillator is coupled to a phase shifter 222 andthen to a modulator 230, both of which are under control of theprocessor subsystem 210. The phase shifter 221 and modulator 230 can becontrolled, in a manner known in the art, to produce the desired pulsesof RF field, for example the excitation and refocusing pulses utilizedin embodiments of the present invention. As described, for example, inU.S. Pat. No. 5,055,788, the oscillator 220 can include a plurality ofoscillators used in a manner that facilitates the generation andultimate detection of the desired signals. The output of modulator 230is coupled, via a power amplifier 235, to an RF antenna 240. A Q-switch250 can be provided to critically damp the RF antenna system to reduceantenna ringing. The antenna 240 is also coupled with a receiver sectionvia a duplexer 265, the output of which is coupled to areceiver/amplifier 270. The duplexer 265 protects the receiver/amplifier270 from high power pulses which pass to the RF antenna 240 during thetransmitting and damping modes.

During the receiving mode, the duplexer 265 is effectively just a lowimpedance connection from the antenna 240 to the receiver amplifier 270.The output of the receiver amplifier 270 is coupled to a dualphase-sensitive detector 275, which also receives, as a reference, asignal derived from the oscillator signal. The detected output iscoupled to an analog-to-digital converter 280, the output of which is adigital version of the received nuclear magnetic resonance signal.

While some embodiments of the invention are described with respect todown-hole or wireline NMR processes, where the substance of interest islocated outside the RF antenna (e.g., outside the coil), otherembodiments of the invention can be applied to a downhole fluid analysis(DFA) technique, including the use of a flow-line analyzer. In suchembodiments, the substance of interest may be located and analyzedinside a coil. In some embodiments, the coil generates a static fieldthat is applied to the substance of interest. Various embodiments of theinvention can yield benefits in such deployments as well as in thedown-hole or wireline NMR processes. Additionally, many of theembodiments disclosed herein can be applied to surface-based NMRtechniques. Even further, aspects of the invention can be applied to anyNMR process performed in an inhomogeneous static magnetic field. Thatis, various embodiments can be applied to NMR processes performedproximate to a substance of interest, where that substance is located inan inhomogeneous magnetic field. Specific examples of NMR processesshould not be considered limiting of the invention described herein.

Refocusing Pulses

Various embodiments of the invention include applying novel types ofcomposite refocusing pulses in an inhomogeneous field, which is atypical condition for NMR well logging. In some embodiments, therefocusing pulses have three segments that take the form of:α_(φ+π)−β_(φ)−α_(φ+π), where α and β are nutation angles for eachsegment and φ is the relative phase of each segment. In someembodiments, two of the segments (e.g., α and α) are of substantiallyequal pulse length. Also, in some embodiments, the middle segment (e.g.,β) is phase shifted approximately 180-degrees from each of the precedingsegment and the following segment (e.g., the middle segment isreverse-phase). According to various embodiments, the phases are notrequired to correspond precisely with the stated values (e.g., 0-degreesor 180-degrees). Small modifications to the phase can be made that willstill achieve some of the advantages of the invention. Furthermore,various embodiments of the present invention are not limited to phaseshifting by 180-degrees. In some embodiments of the present invention,the segments of the refocusing pulse are phase shifted by a differentvalue (e.g., 90-degrees, 150-degrees, 160-degrees or 170-degrees). Anysuch “rotated-phase” refocusing pulses (e.g., 150-degrees or180-degrees) are referred to herein as RPP pulses. Such RPP pulses canreplace the conventional π_(φ)) refocusing pulse in the conventionalCPMG sequence (it is known and referred to herein as 180-degrees).

Three example RPP pulses in accordance with some embodiments of thepresent invention are disclosed, and are referred to as:

RPP 1.0{α,β}≈{0.14π,0.72π}

RPP 1.3{α,β}≈{0.2π,0.9π}

RPP 1.9{α,β}≈{0.3π,1.3π}

It is understood that these pulses are merely example pulses, and that anumber of combinations of a and 0 values can be used in accordance withvarious aspects of the invention. In contrast to the exemplary pulses, aconventional refocusing pulse corresponds to, α=0, β=π and has a totallength of T₁₈₀ (e.g., a rectangular pulse). As used herein, the pulseduration T₁₈₀ is defined as: T₁₈₀=π/(γ×B₁); where γ is the gyromagneticratio of a particle in the substance within the inhomogeneous staticmagnetic field, and B₁ is the maximum amplitude of the applied radiofrequency (RF) field in the area of interest within the substance.Furthermore, as used herein T₉₀ is defined as: T₉₀=π/2(γ×B₁).

FIG. 3 shows graphical representations of respective profiles of a priorart rectangular refocusing pulse (a), and three illustrative RPPrefocusing pulses according to embodiments of the invention (b), (c) and(d) are shown. As shown, the refocusing pulses can utilize the same RFamplitude (y-axis, “A”) as in the prior art refocusing pulse.Illustrative embodiments of the present invention include RPP refocusingpulses with different pulse lengths. For example, the RPP pulses can beof a substantially similar pulse length (x-axis) as the prior art pulse(e.g., RPP-1.0), minimally longer than the prior art pulse (e.g.,RPP-1.3), or minimally shorter than the prior art pulse. In this manner,the RPP pulses require similar power usage and ability to measure shortrelaxation times, as compared to the conventional pulse.

In further illustrative embodiments, a series of refocusing pulses(e.g., RPP pulses) in an NMR sequence is performed in an inhomogeneousstatic magnetic field. Each refocusing pulse in the series of RPP pulseshas at least two segments, indicated by S and a corresponding number inFIG. 3. In the examples of FIG. 3, each RPP pulse is shown includingthree segments, S1, S2 and S3. As noted herein, in some embodiments,each RPP pulse in the series of RPP pulses can have a total pulseduration (a sum of all the segments) less than or equal to approximately1.414 (the square root of 2) times T₁₈₀. For instance, in the case ofRPP-1.0 and RPP-1.3 pulses, the total pulse duration of all threesegments S1, S2 and S3 is approximately 1.0 times T₁₈₀ and approximately1.3 times T₁₈₀, respectively. In the case of the RPP-1.9 pulse, thetotal duration is 1.9×T₁₈₀. In various embodiments, the total pulseduration is less than or equal to 1.0×T₁₈₀, 1.414×T₁₈₀, 2.0×T₁₈₀,4.0×T₁₈₀, or 8.0×T₁₈₀. In other embodiments, the total pulse durationranges between 0.1×T₁₈₀ and 1.0×T₁₈₀.

In some embodiments, each of the at least two segments (e.g., S1, S2,S3) of the RPP pulse can have a phase of either zero degrees or 180degrees. FIG. 3 illustrates that each middle segment S2 in the RPPpulses has a phase of approximately 180 degrees. Each initial (S1) andfinal (S3) segment, respectively, has a phase of approximately0-degrees. Not all phase indicators (e.g., S1 and S3 in FIG. 3(b)) arelabeled for clarity of illustration.

In another illustrative embodiment, the RPP pulse includes two segments.One of the two segments has a phase of 0-degrees and the other segmenthas a phase of 180-degrees (not shown). Such an embodiment has a totalpulse length of less than approximately 1.414×T₁₈₀. In yet anotherillustrative embodiment, the RPP pulse includes four segments. In suchan embodiment, a first and third segment may have phases of 0-degreesand a second and a fourth segment may have phases of 180 degrees (notshown). Various embodiments of the invention may include more than foursegments (e.g., 5, 10, 20 segments) with a number of different types ofphase arrangements. In specific embodiments, the RPP pulses include fouror more segments and the first three segments take the form ofα_(φ+π)−β_(φ)−α_(φ+π), while the segments that follow the first threetake a different form (e.g., constant phase).

In further illustrative embodiments, each of the at least two segments(e.g., S1, S2, S3) of the RPP refocusing pulse has a substantiallyconstant amplitude (e.g., “A” or “−A”). In this case, the term“substantially constant” indicates that the amplitude of each segment ofthe RPP pulse remains within +1-10% of the overall pulse amplitude (A).

The methods according to certain embodiments of the invention canfurther include applying an excitation pulse to the substance within theinhomogeneous static magnetic field prior to applying the series of RPPpulses. Particular excitation pulses, which can be applied prior to theRPP pulses, are described in greater detail with reference to otherembodiments below. It is understood that the overall NMR processaccording to various embodiments can include detecting NMR signals fromthe substance during application of the series of RPP pulses, such thatapplying the RPP pulses allows for data gathering about properties ofthe substance in the inhomogeneous field. In particular, detecting theNMR signals from the substance allows for determination of one or morecharacteristics of the substance.

Another method for applying an NMR sequence, in accordance with oneembodiment, includes applying a series of refocusing pulses (e.g., RPPpulses) to a substance within an inhomogeneous static magnetic field.Referring again to FIG. 3, each of the RPP pulses (e.g., RPP-1.0,RPP-1.3, RPP-1.9, etc.) in the series of pulses includes an initialsegment S1, a middle segment S2 and a final segment S3. In someembodiments, the initial segment S1 and the final segment S3 each havesubstantially equal durations (T_(α)), and the middle segment S2 has adistinct duration (T_(β)) from the initial and final segments S1, S3.Furthermore, the initial segment S1, middle segment S2 and final segmentS3 can have a substantially constant amplitude “A” as defined herein.Additionally, a phase of the middle segment S2 is shifted 180-degreeswith respect to each of the initial segment S1 and the final segment S3.

In one case, a sum of the durations of the initial segment S1 (T_(α)),the middle segment S2 (T_(β)) and the final segment S3 (T_(α)) is lessthan or equal to approximately four times T₁₈₀. In another case, a sumof the durations of the initial segment S1, the middle segment S2, andthe final segment S3 is less than or equal to approximately two timesT₁₈₀. Examples of this scenario are illustrated with respect to RPP-1.9,and RPP-1.3, in FIGS. 3(d) and 3(c), respectively.

In yet another case, a sum of the durations of the initial segment S1(T_(α)), the middle segment S2 (T_(β)), and the final segment S3 (T_(α))is less than or equal to approximately T₁₈₀. One example of thisscenario is illustrated with respect to RPP-1.0 in FIG. 3(b). In thisparticular embodiment (RPP-1.0), each RPP pulse in the series of pulseshas an initial segment S1 and final segment S3 (designated as α), eachwith a duration of approximately 0.14 times T₁₈₀, and a middle segment(designated as β) with a duration of approximately 0.72 times T₁₈₀. Inanother example (RPP-1.3), each RPP pulse in the series of pulses has aninitial segment S1 and final segment S3 (designated as α), each with aduration of approximately 0.2 times T₁₈₀, and a middle segment(designated as β) with a duration of approximately 0.9 times T₁₈₀. FIG.4 shows a graphical representation of combinations of a and (3 values inthe RPP pulses in accordance with certain embodiments of the presentinvention. The areas with larger α and β values (e.g., 2.0, 1.8. versus1.2, 1.4) indicate improved performance relative to the conventionalpulse.

As described herein, various embodiments of the invention are concernedwith determining characteristics of a substance located within aninhomogeneous static magnetic field. The term “inhomogeneous” should beconsidered in the context of the NMR art. Many NMR well logging toolsdeploy inhomogeneous static magnetic fields due to the limitations andconstraints of a borehole environment. In this context, an inhomogeneousstatic magnetic field is a static magnetic field that varies inintensity within an area of interest of a substance. In one example, aninhomogeneous static magnetic field may vary in intensity by a valueapproximately equal to or greater than a nominal amplitude of the seriesof RPP refocusing pulses, denoted as amplitude “A” in FIG. 3.

Illustrative embodiments of the present invention are also directed todetermining characteristics of the refocusing pulses, such as an echoshape and an SNR for the refocusing pulses. The echo shapecharacteristics and the SNR can be used to optimize the refocusingpulses. Optimal control theory (“OCT”) is one tool that can be used todetermine pulse characteristics. In certain embodiments, characteristicsfor several different types of refocusing pulses can be determined andthe refocusing pulses with the most desirable characteristics can beselected for use in an NMR tool. A method and process for determiningrefocusing pulse characteristics follows.

As noted herein, when the Larmor frequencies of spins are substantiallyinhomogeneous, as in, for example, NMR well logging, the spin echoeswithin the substance of interest go through transient states and quicklyapproach asymptotic form. One method for determining an asymptotic echois to let M(O⁺) be the magnetization after the initial excitation pulse,and denote {circumflex over (n)}={circumflex over (n)}(Δω₀, ω₁) as theaxis of the effective rotation that describes the evolution from oneecho to the next for a given value of ω₀, (e.g., the offset in B₀, andω₁), the amplitude of the RF field B₁, and θ the angle of rotation. Themagnetization at the N^(th) echo can be decomposed into 3 components as:

{right arrow over (M)} _(N)=({circumflex over (n)}·{right arrow over(M)}(0⁺)){circumflex over (n)}+cos(Nθ)[{right arrow over(M)}(0⁺)−({circumflex over (n)}·{right arrow over (M)}(0⁺)){circumflexover (n)}]+sin(Nθ)({circumflex over (n)}×{right arrow over(M)}(0⁺))  (1)

In sufficiently inhomogeneous fields and large enough echo numbers N,the second and third terms will average out and the asymptotic echo isgiven solely by the first term as:

{right arrow over (M)} _(asy)(Δω₀,ω₁)=({circumflex over (n)}·{rightarrow over (M)}(0⁺){circumflex over (n)}  (2)

To refocus spins initially along the x direction, a perfect excitationpulse (e.g., M(0±)={circumflex over (x)} for all values of Δ ω₀ and ω₁)can be used. In this case, the expression for the asymptoticmagnetization simplifies to:

{right arrow over (M)} _(asy)(Δω₀,ω₁)=n _(x) ² {circumflex over(x)}  (3)

An advantageous refocusing pulse can display n_(x) ²=1, over a verylarge region of the (Δ ω₀, ω₁) space. FIG. 5 shows a graphicalrepresentation of the distribution of n_(x) ² for a plurality of RPPpulses in accordance with certain embodiments of the present invention.In this example, an echo spacing T_(E) is chosen to be equal to 6×T₁₈₀T_(P), where T_(P) is the corresponding refocusing pulse length. Invarious embodiments of the present invention, the echo spacing T_(E) isthe time period between a central portion of a first echo and a centralportion of second echo. This time T_(E) includes the pulse length T_(P)and a free-precession period T_(FP). Also, in this example, spacingbetween the application of two consecutive refocusing pulses, withoutincluding the refocusing pulse, is chosen to be equal to 6×T₁₈₀ and the“A” is the nominal RF amplitude.

FIG. 5 illustrates n_(x) ² over field inhomogeneities for a conventionalpulse and a plurality of RPP pulses. The sum of n_(x) ² is the maximumpossible normalized magnetization. As shown in the figure, compared tothe conventional pulse, the in-phase magnetization (indicated by darkoutlines) for the RPP pulses is greater in a larger region of fieldinhomogeneities. At the nominal RF frequency, the RPP pulses can focusmore spins far off resonance. In various embodiments, the performance ofthe RPP pulses is slightly inferior in the close vicinity of resonance,but the RPP pulses compensate for this phenomenon with improvedperformance off-resonance.

Asymptotic echo shapes and SNR of the RPP pulses can be determined asfollows. For a field inhomogeneity that is characterized by thedistribution map f(ω₀, Δω₁), the asymptotic echo shape is given by:

M(t)=∫∫dΔω ₀ dω ₁ e ^(iΔω) ⁰ ^(t)(M _(asy,x) +iM_(asy,y))(Δω₀,ω₁)f(Δω₀,ω₁)  (4)

In this case, there is only the in-phase component, so equation (4) issimplified as:

M(t)=∫∫dΔω ₀ dω ₁ e ^(iΔω) ⁰ ^(t) n _(x) ² f(Δω₀,ω₁)  (5)

Using a matched filter and a constant noise spectrum density, the SNR isevaluated as:

SNR∝∫ _(T) _(ac) _(q/2) ^(T) ^(acq) ^(/2) M(t)² dt  (6)

where T_(acq) is the acquisition time. In a constant B₀ gradient f(ω₀, Δω₁)≈const×f₁(ω₁). In that case, the following equation applies:

M(t)=∫dω ₁ f ₁(ω₁)∫dω ₀ e ^(iω) ⁰ ^(t) n _(x) ²(ω₀,ω₁)=∫dω ₁ f ₁(ω₁)m(ω₁,t).  (7)

FIG. 6 shows the echo shape m(ω₁, t) for different values of ω₁. Thisfigure illustrates the asymptotic echo shape for different pulses withRF inhomogeneity, assuming a perfect initial 90-degree pulse. In thiscase, 3126 spins were used in a constant gradient from [−10A, 10A],where “A” is the nominal RF amplitude. The echo peaks for the new RPPpulse are constantly high compared to that of the conventional pulse. Inparticular, the peak for RPP-1.0 increases as the RF amplitudeincreases.

FIG. 7 shows Table 1, which illustrates the SNR for each of theconventional pulse, the RPP-1.0 pulse, the RPP-1.3 pulse, and theRPP-1.9 pulse, under two different initial excitations. The SNR isnormalized with respect to an SNR for a rectangular 180-degreerefocusing pulse with a perfect rectangular 90-degree excitation pulse.

FIG. 8 shows a graphical representation of SNR in the presence of RFinhomogeneity. The SNR for all four pulses is normalized with respect toan SNR for rectangular 180-degree refocusing pulses. In each case, aperfect rectangular 90-degree excitation pulse is used. “A” is thenominal RF amplitude. As shown, given a uniform distribution of RFinhomogeneity, the SNR stays consistently higher for the RPP pulses inthe presence of RF inhomogeneity. In particular, RPP-1.0 is lesssensitive to RF inhomogeneity than the conventional rectangularrefocusing pulses. At 90% RF inhomogeneity, the rectangular pulse loseshalf of the nominal value, while the RPP pulses still produce an SNR 1.5times the nominal value.

In some cases, an improved performance can be achieved by usingexcitation pulses that align initial magnetization with the effectiverefocusing axis n of the refocusing pulses, as shown in Equation 2.Table 1 reports the improved potential performance of the RPP pulses atthe nominal RF amplitude, when the initial magnetization is aligned withthe refocusing axis. As shown, in some cases, the RPP refocusing pulsescan yield a much higher SNR than the conventional rectangular refocusingpulse. This may be a result of, for example, the ability of the RPPpulses to refocus more spins outside the reach of the conventionalrectangular pulse.

FIG. 9 provides an example of an initial excitation pulse for an RPP-1.0refocusing pulse sequence. This example is provided using a nominal RFamplitude of A=5 kHz, T₁₈₀=200 us, and a pulse length of 1 ms. Theexcitation pulse is 20 times as long as a rectangular 90-degree pulse,but, because the excitation pulse is applied once for the acquisition ofthousands of echoes, the difference in length is not a significantdetriment. In combination with a series of RPP-1.0 refocusing pulses,this illustrative pulse produces an SNR that is 1.79 times the value ofSNR for a series of rectangular refocusing pulses with a perfect90-degree excitation.

In practice, the excitation pulse is neither a perfect 90-degree pulsenor is it able to align the spins precisely with their respective axesof rotation. With respect to conventional “non-perfect” excitationpulses currently used in well logging (e.g., a rectangular 90-degreepulse with a reduced free precession time before the first echo ofT₁₈₀/π), the illustrative pulse produces an SNR that is 2.04 times thevalue of the convention pulse (e.g., a 100% improvement overconventional pulses).

The echo shapes of the current implementation and the proposedimplementation are shown in FIG. 10. As shown, FIG. 10 illustrates acomparison of the echo shapes generated from 3126 spins in a constantgradient. The lower solid curve shows the echo shape of the conventionalrefocusing pulse with a rectangular 90-degree pulse and a reduced delayfree precession time T₁₈₀/π. The top solid curve shows the echo shape ofthe RPP-1.0 refocusing pulse when combined with one of the novelexcitation pulses disclosed herein. The solid curves show in-phasecomponents, while dashed curves show out-of-phase components.

In some embodiments, the RPP pulses outperform the conventionalrefocusing pulses in a plurality of aspects. These RPP pulses are ableto focus spins over a thicker slice and are less sensitive to RFinhomogeneity. As a consequence, in some embodiments, the SNR is doubledwhen compared with the conventional refocusing pulses, even in thepresence of large RF inhomogeneity. In this way, the performance of theRPP pulses greatly exceeds that of conventional pulses. This improvedSNR can greatly improve the precision of measurements of porosity, poresize distributions, and other important parameters in petrophysics.

As is also disclosed herein and below, various embodiments of thepresent invention include combinations of excitation pulses with RPPrefocusing pulses.

Excitation Pulses

Various embodiments of the invention are directed to methods forapplying an NMR sequence to determine characteristics of a substancewithin an inhomogeneous static magnetic field. The method includesapplying an excitation pulse to the substance within the inhomogeneousstatic magnetic field to induce a spin effect within the substance. Insuch an embodiment, the excitation pulse includes a plurality ofsegments. The method can further include applying a refocusing cycle tothe substance, where the refocusing cycle generates a magnetization thatis defined by a refocusing axis.

In various embodiments of the present invention, the excitation pulsegenerates an initial magnetization that is aligned with the refocusingaxis of the refocusing pulses. In other words, the excitation pulsegenerates an initial magnetization that is aligned with a refocusingaxis produced by a subsequent refocusing cycle. In contrast, manyconventional systems align the initial magnetization with a transverseplane of a molecular nucleus, without regard for the refocusing axisproduced by the refocusing pulses.

A “refocusing cycle” in this embodiment, and as described herein, isdefined as the duration of the refocusing pulse plus the delay betweenthe refocusing pulse and the next pulse in the sequence.

In various embodiments, application of the excitation pulse is followedby applying RPP refocusing pulses, such as an RPP refocusing pulse thattakes the form of: α_(φ+π)−β_(φ)−α_(φ+π). Furthermore, in someembodiments, following application of the excitation pulse, the methodcan include performing at least ten refocusing cycles (e.g., 100, 1000or 5000 refocusing cycles). The refocusing cycles can be performedsuccessively.

Sequences that include such excitation pulses and/or RPP pulses canimprove the signal-to-noise ratios (SNR) for NMR processes performed ininhomogeneous field environments. Additionally, as described withrespect to the RPP pulses herein, in some cases, the inhomogeneousstatic magnetic field can vary by a value that is greater than or equalto a nominal amplitude of the refocusing cycle.

In some embodiments, the excitation pulses are specifically designed fora particular series of RPP refocusing pulses (e.g., to further enhancedata gathering about a substance in situ). For example, the excitationpulses include a plurality of segments, which in some cases have asubstantially constant amplitude “A” as defined herein. The amplitude ofthe excitation pulses may be chosen to match the amplitude of the RPPrefocusing pulses. In various embodiments of the invention, the totalexcitation pulse duration is at least as long as the echo spacing T_(E)of the refocusing pulses. For example, in some cases, the excitationpulse can have a total duration equal to or greater than approximately8×T₁₈₀. Furthermore, in some embodiments, each of the plurality ofsegments of the excitation pulses include shifted phases (e.g., a phaseof 0-degrees or 180 degrees), as described with respect to the RPPpulses. According to various embodiments, the phases are not required tocorrespond precisely with the stated values (e.g., 0-degrees or180-degrees). Small modifications to the phase can be made that willstill achieve some of the advantages of the invention.

FIG. 11 shows a plot of an excitation pulse (“A”) according to variousembodiments of the invention, where the amplitude and phase of theexcitation pulse are plotted as a function of time. In the specificexample shown in FIG. 11, the excitation pulse corresponds to an echospacing of T_(E)=6×T₁₈₀ T_(P). The excitation pulse includes 100segments having a length of 0.1×T₁₈₀, resulting in a total length of10×T₁₈₀. Illustrated embodiments of the invention rely on phasemodulation, not amplitude modulation, to improve the SNR ratio in an NMRprocess. To this end, the excitation pulse has an amplitude that is heldconstant, while the phase of the excitation pulse is varied from segmentto segment. FIG. 12 shows Table 2, which includes phase values (indegrees) for each segment of excitation pulse A, in accordance withvarious embodiments of the present invention.

FIGS. 13-18 show six more examples of excitation pulses in accordancewith various embodiments of the present invention. FIGS. 13-18 showTables 3-8, which include phase values (in degrees) for each segment ofexcitation pulses B, C, D, E, F and G, respectively. Each of thesegments has a length of 0.1×T₁₈₀. The number of segments from pulse topulse varies. For example, excitation pulse C includes 202 segmentswhile pulse D includes 156 segments. Accordingly, the total duration ofeach excitation pulse also varies. The amplitude is held constantbetween segments in each of the excitation pulse.

Such constant-amplitude excitation pulses are easier to implement inpower-constrained hardware when compared to conventional excitationpulses. Also, as is shown and described herein, such constant-amplitudeexcitation pulses can improve the SNR ratio in an NMR process. FIG. 19shows Table 9, which compares simulated and measured SNR for variousembodiments of the present invention. The first two listed sequences areconventional sequences that use rectangular excitation pulses with90-degree nutation angles. The first-listed conventional sequence usesrefocusing pulses with 180-degree nutation angles, while thesecond-listed conventional sequence uses refocusing pulses with135-degree nutation angles. Table 9 also shows the simulated andmeasured SNR for excitation pulses A-G from FIGS. 11-18. Each excitationpulse is paired with a sequence of RPP-1.0 refocusing pulses. Eachlisted value of the simulated and measured SNR is normalized to thefirst-listed conventional sequence. As shown by Table 9, the SNR foreach of excitation pulses A-G is significantly greater than the SNR forthe two conventional pulse sequences.

Table 9 also shows a theoretical SNR limit for a perfect excitationpulse. Such a perfect excitation pulse aligns every available isochromatalong the CPMG refocusing axis. Such a perfect excitation pulse achievesa theoretical upper limit of 3.31. In accordance with one embodiment ofthe present invention, excitation pulse B achieves an SNR that isapproximately 97% of this upper limit. In this manner, illustrativeembodiments of the present invention increase SNR over conventionalsequences.

Illustrative embodiments of the present invention are also directed todetermining characteristics of the excitation pulses, such as an echoshape and an SNR for the excitation pulses. The echo shapecharacteristics and the SNR can be used to optimize the excitationpulses. For example, characteristics for several different types ofexcitation pulses can be determined and the excitation pulse with themost desirable characteristics can be selected for use in an NMR tool. Amethod and process for determining excitation pulse characteristicsfollows.

Excitation pulses in accordance with various embodiments of theinvention are intended to generate an initial magnetization, M (Δw₀), attime 0⁺, in a substance which is approximately aligned with an effectiverefocusing axis in a refocusing pulse (e.g., a RPP pulse). This isdistinct from the conventional “hard” excitation pulses which generatean initial magnetization on a transverse plane of a molecular nucleus.The inventors have discovered some advantages of the excitation pulseover the conventional hard excitation pulses. For example, excitationpulses can be configured to maximize the amount of asymptoticmagnetization. The asymptotic magnetization is given by: {right arrowover (M)}_(asy)=({right arrow over (M)}(0⁺)·{circumflex over(n)}){circumflex over (n)}, where n is the effective axis of the CPMGrefocusing cycle, and M(O⁺) is the magnetization vector at time 0⁺.Excitation pulses can be configured to maximize the initial dot product,and, as a result, the amount of asymptotic magnetization. The asymptoticechoes actually detected by the coil are produced by the transverseprojection of M_(asy) onto the transverse plane, which is given by:{right arrow over (M)}_(⊥)=({right arrow over (M)}(0⁺)·{circumflex over(n)}){circumflex over (n)}_(⊥), where {circumflex over (n)}_(⊥) is thetransverse component of {circumflex over (n)}. The time domain signalsdetected for “hard” pulses (M(0⁺)=M₀{circumflex over (x)}) andexcitation pulses (M(0⁺)=M₀{circumflex over (n)}) are given by:

$\begin{matrix}{{M_{\bot}(t)} = {\int{{d\left( {\Delta\omega}_{o} \right)}e^{i\; {\Delta\omega}_{o}t}{M_{\bot}\left( {\Delta\omega}_{o} \right)}}}} \\{{= {M_{0}{\int{{d\left( {\Delta\omega}_{o} \right)}e^{i\; {\Delta\omega}_{o}t}{n_{\bot}^{2}\left( {\Delta\omega}_{o} \right)}}}}},{{{when}\mspace{14mu} {\overset{\rightarrow}{M}\left( 0^{+} \right)}} = {M_{0}\hat{x}}}} \\{{= {M_{0}{\int{{d\left( {\Delta\omega}_{o} \right)}e^{i\; {\Delta\omega}_{o}t}{n_{\bot}\left( {\Delta\omega}_{o} \right)}}}}},{{{when}\mspace{14mu} {\overset{\rightarrow}{M}\left( 0^{+} \right)}} = {M_{0}{\hat{n}.}}}}\end{matrix}$

Excitation pulses generate more signal because |n_(⊥)|≦1. Thus,illustrative embodiments of the excitation pulses maximize the SNR ofthe asymptotic echoes for a given refocusing cycle. This cycle istypically repeated many times, and thus determines the peak and averagepower dissipated and total energy consumed by the sequence. As such,illustrative embodiments of the excitation pulses can serve as a generalway to maximize SNR of the CPMG sequence, particularly when subject topower or energy constraints.

It is noteworthy to mention that, because the frequency dependence of{circumflex over (n)}(Δw_(o)) depends upon the echo spacing T_(E), someillustrative embodiments of the excitation pulses are specific for agiven echo spacing, and a particular type of refocusing pulse (e.g., RPPpulses). In one particular embodiment described herein, the excitationpulses are tailored to the RPP-1.0 pulse shown in FIG. 3(b). Forexample, FIGS. 11-18 show excitation pulses A-G that are tailored to theRPP-1.0 refocusing pulse.

In various illustrative embodiments, optimizing processes (e.g., OCT)can be used to determine excitation pulses with advantageous SNR andecho characteristics. In some embodiments, the excitation pulses areoptimized jointly with refocusing pulses (e.g., both the excitationpulses and refocusing pulses include unconstrained variables). In otherembodiments, the excitation pulses and refocusing pulses are optimizedseparately (e.g., either the excitation pulses or the refocusing pulsesinclude entirely constrained variables).

The optimization can be performed using a uniform distribution ofresonance frequency offsets and/or various forms of RF field strengthinhomogeneity. Various different cost functions can be used to optimizethe excitation and refocusing pulses. In some embodiments, a costfunction is used that includes a weighted sum of two properties of anasymptotic echo (e.g., a peak amplitude and a root means squaredintegral). The root means square integral ensures that SNR is maximized,while the peak amplitude biases the optimization towards echoes withdesirable time-domain properties (e.g., localized single peak). In thismanner, the cost function is maximized to find the optimum excitationpulse and/or refocusing pulses.

Within the optimization process, certain constraints can be used to findadvantageous pulses in accordance with embodiments of the presentinvention. For example, one constraint may be that the excitation pulsegenerates an initial magnetization that is aligned with a refocusingaxis of a selected series of refocusing pulses. Additional oralternative limitations can also be used. The following is anon-limiting list of potential constraints:

The excitation pulses include at least two segments;

The refocusing pulses include at least two segments;

The excitation pulse modulates phase between segments;

The refocusing pulse modulates phase between segments;

The excitation pulse is at least as long as the echo spacing T_(E);

The length of the refocusing pulse is less than or equal to T₁₈₀;

The segment length for each segment of the refocusing pulse must bebetween 0.2×T₁₈₀ and 5×T₁₈₀; and/or

The segment length for each segment of the excitation pulse must bebetween 0.2×T₉₀ and 5×T₉₀.

Any or all such constraints can be used to find advantageous pulses inaccordance with embodiments of the present invention. Such optimizationprocesses can be used to optimize any of the excitation and refocusingpulses described herein.

Illustrative embodiments of the present invention are also directed tophase cycling techniques that use a phase inversion process. A generalRF pulse at frequency φw can be defined as:

S(t)=A(t)cos(ω_(RF) t+ω(t)),  (8)

where A(t) and ψ(t) are the instantaneous amplitude and phase of thepulse, respectively. In conventional systems, phase cycling of theexcitation pulses is performed using conventional phase shifting. Inconventional phase shifting, a constant phase φ is added to theinstantaneous phase −ψ(t) of the excitation pulse. The response M ^(φ)of the phase-shifted pulse is simply related to the response M of theoriginal pulse by:

{right arrow over (M)} _(⊥) ^(φ)(Δω₀)=e ^(iφ) {right arrow over (M)}_(⊥)(Δω₀)

{right arrow over (M)} _(z) ^(φ)(Δω₀)={right arrow over (M)}_(z)(Δω₀)  (9)

According to Equation 9, conventional phase shifting rotates thetransverse magnetization by the same amount, and leaves the longitudinalmagnetization unaffected.

Conventional CPMG phase-cycling techniques rely on such conventionalphase shifting. In such techniques, echoes are acquired in a first scanusing a first sequence. Then, the phase of the excitation pulse isshifted by 7 and the sequence is performed in a second scan. Theresultant echoes from the second scan are subtracted from those acquiredfrom the first scan, creating a so-called phase-alternating pair (PAP).The asymptotic magnetization is given by:

{right arrow over (M)} _(PAP)(Δω_(o))={circumflex over (n)}({right arrowover (M)}(0⁺)·{circumflex over (n)})−{circumflex over (n)}({right arrowover (M)} ^(π)(0⁺)·{circumflex over (n)}).  (10)

Here, {circumflex over (n)} is the effective refocusing axis, and M(0⁺)and M ^(π)(0⁺) are the magnetizations produced by the excitation pulsein the first and second scans, respectively. Equation (9) predicts thatthe phase shift inverts the transverse, but not the longitudinalcomponent of the initial magnetization, which is reflected as:

{right arrow over (M)} _(⊥) ^(π)(0⁺)=−{right arrow over (M)} _(⊥)(0⁺).

{right arrow over (M)} _(z) ^(π)(0⁺)=+{right arrow over (M)}_(z)(0⁺)  (10)

The phase cycling cancels the longitudinal portion of the initialmagnetization, and the asymptotic magnetization is given by:

{right arrow over (M)} _(PAP)(Δω_(o))=2{circumflex over (n)}({rightarrow over (M)} _(⊥)(0⁺)·{circumflex over (n)} _(⊥)),  (12)

where {circumflex over (n)}={circumflex over (n)}_(z)+{circumflex over(n)}_(⊥). The projection of M_(PAP) (Δ ω₀) onto the transverse plane isdetected by the coil. In some cases, for excitation pulses according tovarious embodiments of the invention, conventional phase cycling may notbe optimal because only the overlap of the transverse components ofM(Δω₀) with {circumflex over (n)} is retained in the asymptoticmagnetization after phase cycling.

Instead of conventional phase cycling, illustrative embodiments of thepresent invention use a phase inversion process. Refocusing cycles actas composite rotations, which include refocusing pulses and segments offree precession, during which {circumflex over (n)}₁=z₁. In someembodiments, RPP refocusing pulses contain segments with phases of 0 andπ, and so have rotation axes {circumflex over (n)}₂ that are confined tothe {circumflex over (x)}-z plane. Also, in some cases, refocusingcycles are symmetric, which causes the refocusing axis (axis of thecomposite rotation) to lie in the plane spanned by {circumflex over(n)}₁ and {circumflex over (n)}₂, e.g., the {circumflex over (x)}-zplane. It is beneficial to retain both the {circumflex over (x)} and thez components of the magnetization produced by the excitation pulse. Tothis end, illustrative embodiments of the present invention use a phasecycling technique that includes a phase inversion process (e.g.,replacing ψ(t) with −ψ(t)).

In various embodiments, the phase inversion process can be applied asfollows. In accordance with a specific embodiment of the invention,echoes are acquired in a first scan using a first sequence including anexcitation pulse and a series of refocusing pulses. The phase of theexcitation pulse is inverted (e.g., its complex conjugate is formed) andthe sequence is run again in a second scan using the inverted excitationpulse and the series of refocusing pluses. In some embodiments, thesecond scan is performed before the first scan. The resultant echoesfrom the second scan are subtracted from those acquired during the firstscan. The asymptotic magnetization is given by:

{right arrow over (M)} _(PI)(Δω_(o))={right arrow over (n)}({right arrowover (M)}(0⁺)·{right arrow over (n)})−{right arrow over (n)}({rightarrow over (M)} ^(−ψ)(0⁺)·{right arrow over (n)}).  (13)

where M ^(−ψ(t))(Δω₀) is the magnetization produced by thephase-inverted excitation pulse. The {circumflex over (x)} and zcomponents of the magnetization produced by the phase-invertedexcitation pulse are related in a simple way to those produced by theoriginal pulse. In this manner, the following relationships aredetermined:

M _(x) ^(−ψ)(0⁺;Δω_(o))=−M _(x)(0⁺;Δω_(o))

M _(z) ^(−ψ)(0⁺;Δω_(o))=+M _(z)(0⁺;Δω_(o)).  (14)

The {circumflex over (x)} component of the refocusing axis is symmetricabout Δω₀=0, while the z component is anti-symmetric. In this manner,the following relationships are determined:

n _(x)(Δω₀)=n _(x)(−Δω₀)

n _(z)(Δω₀)=−n _(z)(−Δω₀).  (15)

In certain embodiments of the invention, the excitation pulses producemagnetization that matches the refocusing axis, so for some pulses, thesame symmetry relationships apply:

M _(x)(0⁺;Δω_(o))≈M _(x)(0⁺;−Δω_(o))

M _(z)(0⁺;Δω_(o))≈−M _(z)(0⁺;−Δω_(o)).  (16)

Within this approximation, equations (14) and (16) can be used to showthat the asymptotic magnetization after the phase inversion process is:

$\begin{matrix}\begin{matrix}{{{\overset{\rightarrow}{M}}_{PI}\left( {\Delta\omega}_{o} \right)} = {\overset{\rightarrow}{n}\begin{bmatrix}{{\left( {{M_{x}\left( {0^{+};{\Delta\omega}_{o}} \right)} - {M_{x}^{- \psi}\left( {0^{+};{\Delta\omega}_{o}} \right)}} \right)n_{x}} +} \\{\left( {{M_{z}\left( {0^{+};{\Delta\omega}_{o}} \right)} - {M_{z}^{- \psi}\left( {0^{+};{\Delta\omega}_{o}} \right)}} \right)n_{z}}\end{bmatrix}}} \\{= {\overset{\rightarrow}{n}\begin{bmatrix}{{\left( {{M_{x}\left( {0^{+};{\Delta\omega}_{o}} \right)} + {M_{x}\left( {0^{+};{- {\Delta\omega}_{o}}} \right)}} \right)n_{x}} +} \\{\left( {{M_{z}\left( {0^{+};{\Delta\omega}_{o}} \right)} - {M_{z}\left( {0^{+};{- {\Delta\omega}_{o}}} \right)}} \right)n_{z}}\end{bmatrix}}} \\{\approx {2{\overset{\rightarrow}{n}\left\lbrack {{{M_{x}\left( {0^{+};{\Delta\omega}_{o}} \right)}n_{x}} + {{M_{z}\left( {0^{+};{\Delta\omega}_{o}} \right)}n_{z}}} \right\rbrack}}}\end{matrix} & (17)\end{matrix}$

In some embodiments of the present invention, the phase inversionprocess retains both the {circumflex over (x)} and z components of themagnetization produced by the excitation pulses, which results ingreater asymptotic signal as compared with conventional phase cycling.

The phase inversion process can also be applied (e.g., instead of phaseshifting) to various other excitation pulses described herein. Theexcitation pulse can even be used with rectangular π/2 excitationpulses. Doing so, in many cases, is not advantageous because rectangularπ/2 excitation pulses produce longitudinal magnetization that issymmetric about Δω₀=0, i.e., M_(z)(0⁺; −Δω₀). In such cases, phaseinversion will cancel out the z component, as shown by equation (17).

FIG. 20 shows plots of an asymptotic magnetization signal and atime-domain echo signal in accordance with various embodiments of thepresent invention. The top plot shows asymptotic magnetization signalsproduced by a phase inversion process and a conventional phase shiftingprocess (e.g., shifting the phase by π). The pulse sequence used foreach case includes excitation pulse A, as shown in FIGS. 11 and 12, anda series of RPP-1.0 refocusing pulses, as shown in FIG. 3. The bottomplot shows time-domain echo signals produced by the phase inversionprocess and the conventional phase shifting process. As can be seen fromthe plot, the phase inversion process produces a significantly largersignal in each case.

The excitation pulses and/or the phase inversion processes performed inaccordance with various embodiment of the present invention cansignificantly improve SNR for NMR processes performed in inhomogeneousfield environments. In some cases, various embodiments of the presentinvention include SNRs (in power units) are 3.2 times higher thanconventional sequences. As a result, the time required to obtain a givenSNR is reduced by a similar factor.

Additional or Alternative Excitation Pulses

In yet another embodiment of the present invention, a method forapplying an NMR sequence includes applying an excitation pulse to asubstance within an inhomogeneous static magnetic field, followed byapplying a series of refocusing pulses to the substance. The excitationpulse is applied to induce a spin effect within the substance, as inconventional approaches. In contrast to conventional approaches, variousembodiments of the invention include applying an excitation pulse havinga plurality of segments with a substantially constant amplitude, whereeach of the segments has one phase selected from no more than twodistinct phases. As described herein, this embodiment allows forapplication of excitation and refocusing pulses using NMR equipmentwhich may lack capability to switch between many different phases. Thus,illustrative embodiments of the present invention advantageously allowfor application of the pulses described herein using existing NMRhardware, without the need for retrofitting or upgrading of hardware.

In various embodiments of the present invention, an excitation pulseshas N segments. The RF amplitude and phase is constant within each ofthe segments, but can vary across segments. The length of the n-thsegment is T_(n). In some embodiments, for the purposes of simplifyinghardware implementations, all segments can have the same RF amplitude.In these cases, this constant RF amplitude can be approximately equal tothat of the refocusing pulses (e.g., the selected RPP pulses).

Additionally, various embodiments of these excitation pulses modulatethe RF phases of each of the segments between two distinct phases: (a)approximately φ+π/2; and (b) approximately φ+3π/2, where   is the phasefor a series of subsequent refocusing pulses. In further illustrativeembodiments, the excitation pulses include segments with alternatephases that differ by π and the segments include an arbitrary phaseshift φ₀ relative to the refocusing pulses. In further specificembodiments, the arbitrary phase shift φ₀ is a multiple of π/2. In yetfurther illustrative embodiments, the segments do not include anarbitrary phase shift (e.g., φ₀=0). In various embodiments, such phasemodulation between segments provides improved echo characteristics.Furthermore, according to various embodiments, the phases are notrequired to correspond precisely with the stated phases (e.g., π, π/2,φ+π/2, or φ+3π/2). Small modifications to the phase can be made thatwill still achieve some of the advantages of the invention.

In certain embodiments of the present invention, the excitation pulsesare composed of a plurality of segments (e.g., 10, 20, 100 or 200segments). Additionally, in some embodiments, the excitation pulse canhave a duration greater than or equal to approximately nine times T₁₈₀.These examples should not be construed as limiting the scope of theinvention.

In some cases, application of such an excitation pulse is followed byapplying refocusing pulses as described herein, such as an RPPrefocusing pulse that takes the form of: α_(φ+π)−β_(φ)−α_(φ+π). In oneparticular embodiment, RPP-1.0 refocusing pulses are applied inrefocusing cycles following application of the excitation pulse. In thiscase, as described with respect to the RPP pulses above, each refocusingpulse in the cycle can include an initial segment α and a final segmentα, each having equal durations. Each RPP pulse can further include amiddle segment β having a duration distinct from the initial segment andfinal segment. The initial segment, middle segment and final segmenthave a substantially constant amplitude. Furthermore, the phase of themiddle segment is shifted 180 degrees with respect to each of theinitial segment and the final segment.

In various embodiments, following application of the excitation pulse,the method can include performing at least ten refocusing cycles (e.g.,100, 1000 or 5000 refocusing cycles). The refocusing cycles can beperformed successively, and each can last for approximately the durationof the refocusing pulse plus the delay between the refocusing pulse andthe next pulse (e.g., the next refocusing pulse) in the sequence.

Tables 10 and 11 in FIGS. 21 and 22 show excitation pulses in accordancewith various embodiments of the present invention. Table 10 (FIG. 21)illustrates the segment lengths of several excitation pulses inaccordance with various embodiments of the present invention: CP-M8,CP-M10, CP-M12, and CP-M15. All segment lengths in Table 2 arenormalized to the length of a rectangular 90-degree pulse at the same RFpower level. With the exception of CP-M12, which has 10 segments, eachexcitation pulse has 20 segments. The total pulse lengths are listed atthe bottom of Table 10. The excitation pulses are optimized for use withan RPP-1.0 refocusing pulse. The excitation pulses include segmentphases that alternate between φ+π/2 and φ+3π/2, while the RPP-1.0segment phases alternate between φ and φ+π.

Table 11 (FIG. 22) shows a summary of values of a squared echo integralproduced by the excitation pulses described in Table 10 (FIG. 21). Inorder to create this table, the excitation pulses were used in CPMGsequences, and the squared integral of the asymptotic echo wascalculated. That squared integral of the asymptotic echo was thennormalized to the default case of rectangular excitation and refocusingpulses at the same RF power level. Additionally, the half-powerbandwidth of the echoes was calculated and included in Table 11. Asshown, the CP-M8 and CP-M15 excitation pulses achieved the bestperformance.

FIG. 23 illustrates a graphical representation of segment number plottedby segment length for the CP-M8 and CP-M15 excitation pulses,respectively. The CP-M8 and CP-M15 excitation pulses have very similarsegment lengths and total lengths (e.g., 12.33×T₉₀ and 12.39×T₉₀,respectively).

FIG. 24 shows a plot of a squared echo integral for a conventionalrefocusing pulse and for a plurality of refocusing pulses in accordancewith various embodiments of the invention. The squared echo integral isplotted as a function of a ratio of refocusing pulse length toexcitation pulse length (e.g., refocusing pulse length/excitation pulselength). In this plot, the excitation and refocusing pulses are assumedto have the same RF power level and the excitation pulse length isfixed, while the length of the refocusing pulse is varied. Additionally,the results have been normalized to those obtained with rectangularpulses at a ratio of 2 (e.g., T₁₈₀/T₉₀).

In FIG. 24, a “stretched” or “squeezed” version of the RPP-1.0 pulse wasused. In other words, the segment lengths were modified in proportion tothe total pulse length. The plot shows that the maximum signal energyfor rectangular pulses occurs at approximately a ratio of 1.5, and isabout 12% higher than the default case at a ratio of 2. This behaviorexplains why NMR well logging tools often use a ratio of approximately1.5. The plot also shows that the signal energy for the RPP and the CP-Mpulses increases monotonically with pulse length for the ratio is lessthan 3 (e.g., between 2 and 3), before saturating at a maximum value.

As explained above, illustrative embodiments of the present inventionare also directed to optimizing excitation pulses using optimizingprocesses. Optimizing processes (e.g., OCT) can be used to determineexcitation pulses with advantageous SNR and echo characteristics. Invarious embodiments, desirable excitation pulses are determined bymaximizing the asymptotic CPMG echoes produced by excitation pulses andrefocusing pulses. To this end, various constraints can be used to findadvantageous pulses in accordance with embodiments of the presentinvention. In one example, the segments of the excitation pulse areconstrained so that they modulate between two distinct phases: (a)φ+π/2; and (b) φ+3π/2. As explained above, in various embodiments, thisform of phase modulation between segments provides improved echocharacteristics.

In another example, the excitation pulse length can be restricted to aparticular number of segments (e.g., no greater than 100 segments). As apractical matter, the use of a large number of segments may not bedesirable because optimizing the pulses becomes much harder as thenumber of search dimensions increases.

In yet another example, the amplitude of the segments of the excitationpulses is constrained so that it is constant within the pulse. Thisconfiguration simplifies hardware implementation and limits peak powerconsumption.

In a further example, the excitation pulse segment lengths areconstrained to a particular range. In various embodiments of theinvention, excitation pulse segment lengths are the single optimizationvariables (e.g., all other variables are fixed).

The following is a non-limiting list of additional potential constraintsfor the optimization process:

All segments of the excitation pulse have a constant amplitude;

The amplitude of the excitation pulse is equal to the amplitude of therefocusing pulses;

The excitation pulse has a constant phase within pulse segments;

The excitation pulse modulates phase between segments;

The excitation pulse is at least as long as the echo spacing T_(E);

The segments of the excitation pulse module between phases having amultiple of π/2;

The segments of the excitation pulse module between no more than twophases;

The segments of the excitation pulse modulate between two distinctphases: (a) φ+π/2; and (b) φ+3π/2; and/or

The excitation pulse is no longer than 100×T₉₀.

Any or all such constraints can be used to find advantageous pulses inaccordance with embodiments of the present invention.

An NMR process (including CPMG sequencing) according to embodiments ofthe present invention may include detecting NMR signals from thesubstance during application of the series of refocusing pulses, suchthat applying the refocusing pulses allows for data gathering aboutproperties of the substance in the inhomogeneous static magnetic field.In particular, detecting the NMR signals from the substance allows fordetermination of one or more characteristics of the substance in situ.Determination of these characteristics is enhanced by use of one or moreof the excitation pulses and refocusing pulses in accordance withembodiments of the present invention.

FIG. 25 shows a flow diagram illustrating processes in a methodaccording to various embodiments of the invention. As described withrespect to various aspects of the invention, a method can include thefollowing processes:

Process P1: Applying an excitation pulse to a substance in aninhomogeneous magnetic field. The excitation pulse can take the form ofany excitation pulse described with respect to the embodiments of theinvention. In some cases, the excitation pulse generates an initialmagnetization aligned with a refocusing axis to be produced by arefocusing cycle performed after the excitation pulse. In variousembodiments, the excitation pulse includes a plurality of segments,where each of the segments has a substantially constant amplitude andeach of the segments has one phase selected from no more than twodistinct phases.

Process P2: Following application of the excitation pulse, process P2can include applying a series of refocusing pulses to the substancewithin the inhomogeneous magnetic field. The series of refocusing pulsescan take the form of any refocusing pulses described with respect to theembodiments of the invention, and can include, for example, one or moreof the RPP pulses described herein.

Process P3: Concurrently with or following application of the series ofrefocusing pulses, process P3 can include detecting NMR signals from thesubstance within the inhomogeneous field. These NMR signals can besubsequently analyzed according to conventional methods.

It is understood that processes P1, P2, P3 and/or any other processesdescribed herein according to the various aspects of the invention canbe implemented utilizing one or more computing devices. In oneembodiment discussed further herein, an aspect of the invention includesa computing device configured to perform one or more of the herein-notedprocesses. In still another embodiment, a computer-readable medium isdisclosed including program code having instructions for performing oneor more of the herein-noted processes when executed on a computingdevice.

FIG. 26 depicts an illustrative environment 101 for performing the NMRprocesses described herein with respect to various embodiments. To thisextent, the environment 101 includes a computer system 102 that canperform one or more processes described herein in order to determinecharacteristics of a substance, e.g., within an inhomogeneous staticmagnetic field. In particular, the computer system 102 is shown asincluding an NMR system 150, which makes computer system 102 operable todetermine characteristics of a substance by performing any/all of theprocesses described herein and implementing any/all of the embodimentsdescribed herein.

The computer system 102 is shown including a processing component 104(e.g., one or more processors), a storage component 106 (e.g., a storagehierarchy), an in-put/output (I/O) component 108 (e.g., one or more I/Ointerfaces and/or devices), and a communications pathway 110. Ingeneral, the processing component 104 executes pro-gram code, such asthe NMR system 150, which is at least partially fixed in the storagecomponent 106. While executing program code, the processing component104 can process data, which can result in reading and/or writingtransformed data from/to the storage component 106 and/or the I/Ocomponent 108 for further processing. The pathway 110 provides acommunications link between each of the components in the computersystem 102. The I/O component 108 can comprise one or more human I/Odevices, which enable a user 112 to interact with the computer system102 and/or one or more communications devices to enable a system user112 to communicate with the computer system 102 using any type ofcommunications link. To this extent, the NMR system 150 can manage a setof interfaces (e.g., graphical user interface(s), application programinterface, etc.) that enable human and/or system users 112 to interactwith the NMR system 150. Further, the NMR system 150 can manage (e.g.,store, retrieve, create, manipulate, organize, present, etc.) data, suchas NMR data 160 (including NMR signal data) using any solution. The NMRsystem 150 can also communicate with a conventional externalinput/output (I/O) device 120 and/or a conventional external storagesystem 122 to read/write data (e.g., NMR data 160). The NMR system 150can additionally communicate with an NMR apparatus 170, which caninclude any conventional NMR hardware and/or software capable ofgenerating a static magnetic field, providing pulses according toinstructions from the NMR system 150, obtaining NMR signal data, etc.

In any event, the computer system 102 can comprise one or more generalpurpose computing articles of manufacture (e.g., computing devices)capable of executing program code, such as the NMR system 150, installedthereon. As used herein, it is understood that “program code” means anycollection of instructions, in any language, code or notation, thatcause a computing device having an information processing capability toperform a particular function either directly or after any combinationof the following: (a) conversion to another language, code or notation;(b) reproduction in a different material form; and/or (c) decompression.To this extent, the NMR system 150 can be embodied as any combination ofsystem software and/or application software.

Further, the NMR system 150 can be implemented using a set of modules132. In this case, a module 132 can enable the computer system 102 toperform a set of tasks used by the NMR system 150, and can be separatelydeveloped and/or implemented apart from other portions of the NMR system150. As used herein, the term “component” means any configuration ofhardware, with or without software, which implements the functionalitydescribed in conjunction therewith using any solution, while the term“module” means program code that enables the computer system 102 toimplement the functionality described in conjunction therewith using anysolution. When fixed in a storage component 106 of a computer system 102that includes a processing component 104, a module is a substantialportion of a component that implements the functionality. Regardless, itis understood that two or more components, modules, and/or systems mayshare some/all of their respective hard-ware and/or software. Further,it is understood that some of the functionality discussed herein may notbe implemented or additional functionality may be included as part ofthe computer system 102.

When the computer system 102 comprises multiple computing devices, eachcomputing device may have only a portion of NMR system 150 fixed thereon(e.g., one or more modules 132). However, it is understood that thecomputer system 102 and NMR system 150 are only representative ofvarious possible equivalent computer systems that may perform a processdescribed herein. To this extent, in other embodiments, thefunctionality provided by the computer system 102 and NMR system 150 canbe at least partially implemented by one or more computing devices thatinclude any combination of general and/or specific purpose hardware withor without program code. In each embodiment, the hardware and programcode, if included, can be created using conventional engineering andprogramming techniques, respectively.

Regardless, when the computer system 102 includes multiple computingdevices, the computing devices can communicate over any type ofcommunications link. Further, while performing a process describedherein, the computer system 102 can communicate with one or more othercomputer systems using any type of communications link. In either case,the communications link can comprise any combination of various types ofwired and/or wireless links; comprise any combination of one or moretypes of networks; and/or utilize any combination of various types oftransmission techniques and protocols.

The computer system 102 can obtain or provide data, such as NMR data 160using a variety of different solutions. The computer system 102 cangenerate NMR data 160, from one or more data stores, receive NMR data160, from another system such as an NMR apparatus 170, the external I/Odevice 120 and/or the external storage system 122, send NMR data 160 toanother system, etc.

While shown and described herein as a method and system for determiningcharacteristics of substances, it is understood that aspects of theinvention further provide various alternative embodiments. For example,in one embodiment, the invention provides a computer program fixed in atleast one computer-readable medium, which when executed, enables acomputer system to determine characteristics of substances. To thisextent, the computer-readable medium includes program code, such as theNMR system 150 (FIG. 26), which implements some or all of the processesand/or embodiments described herein. It is under-stood that the term“computer-readable medium” comprises one or more of any type of tangiblemedium of expression, now known or later developed, from which a copy ofthe program code can be perceived, reproduced, or otherwise communicatedby a computing device. For example, the computer-readable medium cancomprise: one or more portable storage articles of manufacture; one ormore memory/storage components of a computing device; paper; etc.

In another embodiment, the invention provides a method of providing acopy of program code, such as the NMR system 150 (FIG. 26), whichimplements some or all of a process described herein. In this case, acomputer system can process a copy of program code that implements someor all of a process described herein to generate and transmit, forreception at a second, distinct location, a set of data signals that hasone or more of its characteristics set and/or changed in such a manneras to encode a copy of the program code in the set of data signals.Similarly, an embodiment of the invention provides a method of acquiringa copy of program code that implements some or all of a processdescribed herein, which includes a computer system receiving the set ofdata signals described herein, and translating the set of data signalsinto a copy of the computer program fixed in at least onecomputer-readable medium. In either case, the set of data signals can betransmitted/received using any type of communications link.

In still another embodiment, the invention provides a method ofgenerating a system for determining characteristics of substances. Inthis case, a computer system, such as the computer system 102 (FIG. 26),can be obtained (e.g., created, maintained, made available, etc.) andone or more components for performing a process described herein can beobtained (e.g., created, purchased, used, modified, etc.) and deployedto the computer system. To this extent, the deployment can comprise oneor more of: (1) installing program code on a computing device; (2)adding one or more computing and/or I/O devices to the computer system;(3) incorporating and/or modifying the computer system to enable it toperform a process described herein; etc.

The invention has been described with reference to particularembodiments, but variations within the spirit and scope of the inventionwill occur to those skilled in the art. For example, it will beunderstood that other suitable pulse sequences can be employed. Also, itwill be understood that the techniques described herein according toembodiments can be used in combination with other measurements andtechniques, including but not limited to, measurement of relaxationrates, spectroscopy, diffusion constant and other pulse field gradientmeasurements. Furthermore, the process for determining optimalrefocusing and excitation pulses described herein extends to other cases(e.g., joint optimization of both the excitation and refocusing pulsesin an arbitrary distribution of resonance frequencies and RF fieldstrengths).

We claim:
 1. A method for applying a nuclear magnetic resonance (NMR)sequence, the method comprising: applying a series of refocusing pulsesto a substance within an inhomogeneous static magnetic field, eachrefocusing pulse in the series of refocusing pulses having: at least twosegments; and a total pulse duration less than or equal to approximately1.414 times T₁₈₀.
 2. The method of claim 1, wherein each of the at leasttwo segments has a phase of either approximately zero degrees orapproximately 180 degrees.
 3. The method of claim 1, wherein each of theat least two segments has a substantially constant amplitude.
 4. Themethod of claim 1, further comprising: applying an excitation pulse tothe substance, wherein the application of the excitation pulse isperformed prior to the application of the series of refocusing pulses.5. The method of claim 4, further comprising: detecting nuclear magneticresonance signals from the substance during the application of theseries of refocusing pulses.
 6. A method for applying a nuclear magneticresonance (NMR) sequence, the method comprising: applying a series ofrefocusing pulses to a substance within an inhomogeneous static magneticfield, each refocusing pulse in the series of refocusing pulses having:an initial segment and a final segment each having substantially equaldurations; and a middle segment having a duration, wherein each of theinitial segment, the middle segment, and the final segment has asubstantially constant amplitude and wherein a phase of the middlesegment is shifted approximately 180 degrees with respect to a phase ofeach of the initial segment and the final segment.
 7. The method ofclaim 6, further comprising: applying an excitation pulse to thesubstance within the inhomogeneous static magnetic field, wherein theapplication of the excitation pulse is performed prior to theapplication of the series of refocusing pulses.
 8. The method of claim6, wherein the inhomogeneous static magnetic field varies by a valueapproximately greater than or equal to a nominal amplitude of the seriesof refocusing pulses.
 9. The method of claim 6, wherein a sum of thedurations of the initial segment, the middle segment, and the finalsegment is less than or equal to approximately four times T₁₈₀.
 10. Themethod of claim 6, wherein a sum of the durations of the initialsegment, the middle segment, and the final segment is less than or equalto approximately two times T₁₈₀.
 11. The method of claim 6, wherein asum of the durations of the initial segment, the middle segment, and thefinal segment is less than or equal to approximately T₁₈₀.
 12. Themethod of claim 11, wherein the durations of the initial and finalsegments are approximately 0.14 times T₁₈₀ and the duration of themiddle segment is approximately 0.72 times T₁₈₀.
 13. The method of claim6, further comprising: detecting nuclear magnetic resonance signals fromthe substance during the application of the series of refocusing pulses.14. The method of claim 13, further comprising: determining acharacteristic of the substance from the nuclear magnetic resonancesignals.